from what I understand the brass is stronger in regards to abuse... being stepped on, shaken, thrown around in an ammo can. the pressures generated by limited case capacity will exceed .308 by a few thousand with the same powder charge... and while the brass is stronger, it in itself will push the charge up in PSI enough to negate that difference. load down to the beginning loads in .308 using the slower burning powders, seat the bullets long as you can, and remember that LOADING DOWN IS A GOOD THING when it means not only failing to EXPLODE your rifle, but also to limit recoil and conserve your powder by using smaller charges. I've noticed that for my Sierra hpbt 168grs (or 165, can't remember at the moment) I limited recoil by moving down from 45grs Varget to 43.4grs Varget using .308 winchester brass and winchester lrprimers. recoil went from sharp and a bit painful to softer- more of a push and jiggle. I think that if you step down to the beginning load in .308 for a slow powder WITH A LIGHT BULLET then you should be alright (lighter bullets take less thrust to get going, keeping the pressure spike down). also, clean your barrel meticulously between testing every new load, use good/new brass, don't go over starting loads for .308 for your nato's.
let me know if my advise works for you (I don't use military brass since I'm fine with downloaded .308- no need for me to use "tougher" brass since I won't abuse my guns or ammo)